Math Help on equations and number line.?

Question

-n/2 < 3 or 2n-3>12

My answer is N>-6 or N>7 1/2. I think this is right. I'm not sure when I put it on the number line if it's a trick. Do I put a solid circle on 7 1/2? Because if I put an open circle on -6 and draw the arrow right, then I'm thinking that because it is "or" it could include 7 1/2. Hmmmm

Answer 1

You solved the inequalities correctly, which means that:
N > -6 -OR- N > 7.5

This is equivalent to simply: N > -6

If N is greater than -6, then it may or may not be greter than 7.5.
If it is greater than 7.5, it is definitely greater than -6.
So just saying "N > -6" covers all the possibilities in the "or" of the above mathematical statement.

Answer 2

You are correct in that -n/2 < 3 gives n > -6 and 2n - 3 > 12 gives n > 7.5. Because the former includes the latter then they combine to one answer of n > -6. The result is open circle on
-6 and an arrow to the right and that is all. You need put nothing on 7.5.
Having said that, I think that it is a strange problem which would produce the two inequalities with which you started.
It would be useful to check that one of them is not the wrong way round.

Answer 3

Normally, "or" means that you only need to satisfy one condition.

-n/2 < 3 then
-n < 6
n > -6
An open circle on -6 (because -6 does not satisfy the inequality) with the line going to the "right", i.e., towards more positive values, all the way to infinity.

or

2n -3 > 12
2n > 15
n > 7.5 (already included in the preceding answer).

Therefore, I would simply not put any kind of circle at 7.5 because it is already included in the preceding solution.

It is like building a system with two thermostats so that the air conditioning kicks in if the temperature is more than 60F "or" if the temperature is more than 75F. The second thermostat is useless.

The set of answers that satisfy your system of (2) inequalities is (-6, infinity).

Answer 4

Open circles with < & >.
Solid circles with ≤ & ≥.